Confidence Region for Distributed Stochastic Optimization Problem in Stochastic Gradient Tracking Method

Since stochastic approximation (SA) based algorithms are easy to implement and need less memory, they are very popular in distributed stochastic optimization problems. Many works have focused on the consistency of the objective values and the iterates returned by the SA based algorithms. It is of fundamental interest how to quantify the uncertainty associated with … Read more

Discrete Approximation Scheme in Distributionally Robust Optimization

Discrete approximation which is the prevailing scheme in stochastic programming in the past decade has been extended to distributionally robust optimization (DRO) recently. In this paper we conduct rigorous quantitative stability analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined through … Read more

Primal-Dual Hybrid Gradient Method for Distributionally Robust Optimization Problems

We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal-dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition … Read more

Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more